Multiscale Modeling &Simulation, Volume 19, Issue 1, Page 208-241, January 2021.
In this work, cascading transmission line failures are studied through a dynamical model of the power system operating under fixed conditions. The power grid is modeled as a stochastic dynamical system where first-principles electromechanical dynamics are excited by small Gaussian disturbances in demand and generation around a specified operating point. In this context, a single line failure is interpreted in a large deviation context as a first escape event across a surface in phase space defined by line security constraints. The resulting system of stochastic differential equations admits a transverse decomposition of the drift, which leads to considerable simplification in evaluating the quasipotential (rate function) and, consequently, computation of exit rates. Tractable expressions for the rate of transmission line failure in a restricted network are derived from large deviation theory arguments and validated against numerical simulations. Extensions to realistic settings are considered, and individual line failure models are aggregated into a Markov model of cascading failure inspired by chemical kinetics. Cascades are generated by traversing a graph composed of weighted edges representing transitions to degraded network topologies. Numerical results indicate that the Markov model can produce cascades with qualitative power law properties similar to those observed in empirical cascades.

中文翻译：

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用于模拟级联输电线路故障的动力学蒙特卡罗方法

多尺度建模与仿真，第 19 卷，第 1 期，第 208-241 页，2021 年 1 月。
在这项工作中，通过在固定条件下运行的电力系统的动力学模型来研究级联输电线路故障。电网被建模为随机动力系统，其中第一性原理机电动力学由在指定工作点附近的需求和发电中的小高斯扰动激发。在这种情况下，单线故障在大偏差上下文中被解释为跨过由线路安全约束定义的相空间中的表面的第一次逃逸事件。由此产生的随机微分方程系统允许漂移的横向分解，这导致在评估准势（速率函数）以及退出率的计算方面相当简单。受限网络中传输线故障率的易处理表达式源自大偏差理论论证，并针对数值模拟进行了验证。考虑了对现实设置的扩展，并将单个线路故障模型聚合为受化学动力学启发的级联故障的马尔可夫模型。级联是通过遍历由表示向退化网络拓扑的转换组成的加权边组成的图来生成的。数值结果表明，马尔可夫模型可以产生具有与经验级联中观察到的相似的定性幂律特性的级联。和单个线路故障模型被聚合成一个受化学动力学启发的级联故障的马尔可夫模型。级联是通过遍历由表示向退化网络拓扑的转换的加权边组成的图来生成的。数值结果表明，马尔可夫模型可以产生具有与经验级联中观察到的相似的定性幂律特性的级联。和单个线路故障模型被聚合成一个受化学动力学启发的级联故障的马尔可夫模型。级联是通过遍历由表示向退化网络拓扑的转换组成的加权边组成的图来生成的。数值结果表明，马尔可夫模型可以产生具有与经验级联中观察到的相似的定性幂律特性的级联。